The Atkinson Index [1]} measures income inequality and is useful in identifying the end of the distribution that contributes the most towards the observed inequality. Formally, it is defined as
\(A_\epsilon =\begin{dcases}1 - \frac{1}{\bar{\ell }}\biggl (\frac{1}{N}\sum _{i=1}^N \ell _i^{1-\epsilon }\biggr )^{\frac{1}{1-\epsilon _{at}}},& \text{for } 0 \le \epsilon _{at} \ne 1,\\1 - \frac{1}{\bar{\ell }}\biggl (\frac{1}{N}\prod _{i=1}^N \ell _i\biggr )^{\frac{1}{N}},& \text{for } \epsilon _{at} = 1,\end{dcases}\) 
